Song: The Dead Waltz — Radical Face (Song)
Link (YouTube, etc): https://www.youtube.com/watch?v=NkD7LfHk5r0
Lyrics link: https://genius.com/Radical-face-the-dead-waltz-lyrics
Genre: Folk

Song: Would You Fight For My Love? — Jack White (Video)
Link (YouTube, etc): https://www.youtube.com/watch?v=MQOnbp_DspY
Lyrics link: https://genius.com/Jack-white-would-you-fight-for-my-love-lyrics
Genre: Blues/Blues Rock/Alternative Rock

Song: Lay Down in the Tall Grass — Timber Timbre (Song)
Link (YouTube, etc): https://www.youtube.com/watch?v=PpDrhiHepFk
Lyrics link: https://genius.com/Timber-timbre-lay-down-in-the-tall-grass-lyrics
Genre: Folk/Freak Folk/Blues/Southern Gothic (according to wikipedia)

Song: Pillars of Salt — Murder By Death (Song)
Link (YouTube, etc): https://www.youtube.com/watch?v=6Au8kZdNdFU
Lyrics link: https://genius.com/Murder-by-death-pillars-of-salt-lyrics
Genre: Indie Rock/Indie Folk

Song: Secret — The Pierces (Video)
Link (YouTube, etc): https://www.youtube.com/watch?v=HzNFwxsSPwU
Lyrics link: https://genius.com/The-pierces-secret-lyrics
Genre: Indie Pop

Song: Westfall — Okkervil River (Song)
Link (YouTube, etc): https://www.youtube.com/watch?v=TAn2PKDXvdw
Lyrics link: https://genius.com/Okkervil-river-westfall-lyrics
Genre: Folk Rock/Indie Rock

Song: Time Jesum Transeuntum Et Non Riverentum — Nick Cave and Dirty Three (Song)
Link (YouTube, etc): https://www.youtube.com/watch?v=5B2F7_g3a-g
Lyrics link: https://genius.com/Nick-cave-and-the-bad-seeds-time-jesum-transeuntum-et-non-riverentum-lyrics
Genre: Instrumental Rock/Post Rock (according to the Dirty Three wiki page at least)